Question

Suppose B(t) is the balance on your five-year car loan. B is in dollars, t is in years. B(O) -Bo is the purchase price (including tax, registration, warranties, spoiler, alloy wheels, moon roof, etc.) B(5)-0, since the loan is to be paid off in five years. Your credit history scored you a nominal annual interest rate (compounded continuously) of 5%. Even though you make your monthly payment once per month, let's assume for simplicity that you pay continuously at a rate of u dollars per month. a. A differential equation to model the remaining balarce owed is dB/dt-0.05B M FindMin toms of mndfs o b. Identify a quantity undergoing exponential growth/decay, and use this observation to solve for B(t) in terms of μ, Bo and t. c. Suppose you want a nice car, but not over-the-top awesome, such that Bo-40,000. What will the monthly payment be to pay off the loan in five years?

Answer 1

Latar t-, balance =D At t= 1 yr B ( 2 teo 02 3 (It Too

too 4- 3 Balance-B(5) 2 3

1レ2 General プ. t- 七

dl oS eA 七 log (Fos) =

uitth pasin est 七 ! 1.65-1 1:05